51�������

Abstract:

Non-Abelian anyons, a promising platform for fault-tolerant topological quantum computation, adhere to the charge super-selection rule (cSSR), which imposes restrictions on physically allowed states and operations. However, the ramifications of cSSR and fusion rules in anyonic quantum information theory remain largely unexplored. In this study, we unveil that the information-theoretic characteristics of anyons diverge fundamentally from those of non-anyonic systems such as qudits, bosons, and fermions and display intricate structures. In bipartite anyonic systems, pure states may have different marginal spectra, and mixed states may contain pure marginal states. More striking is that in a pure entangled state, parties may lack equal access to entanglement. This entanglement asymmetry is manifested in quantum teleportation employing an entangled anyonic state shared between Alice and Bob, where Alice can perfectly teleport unknown quantum information to Bob, but Bob lacks this capability. These traits challenge conventional understanding, necessitating new approaches to characterize quantum information and correlations in anyons. We expect that these distinctive features will also be present in non-Abelian lattice gauge field theories. Our findings significantly advance the understanding of the information-theoretic aspects of anyons and may lead to realizations of quantum communication and cryptographic protocols where one party holds sway over the other.Comment: 5+9 pages, 1+10 figures, comments are welcome

Abstract:

Photonic qubits play an instrumental role in the development of advanced quantum technologies, including quantum networking, boson sampling and measurement based quantum computing. A promising framework for the deterministic production of indistinguishable single photons is an atomic emitter coupled to a single mode of a high finesse optical cavity. Polarisation control is an important cornerstone, particularly when the polarisation defines the state of a quantum bit. Here, we propose a scheme for producing bursts of polarised single photons by coupling a generalised atomic emitter to an optical cavity, exploiting a particular choice of quantisation axis. In connection with two re-preparation methods, simulations predict ten-photon bursts coincidence count rates on the order of 1 kHz with single $^{87}\mathrm{Rb}$ atoms trapped in a state of the art optical cavity. This paves the way for novel n-photon experiments with atom-cavity sources.